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Embeddings of ℂ*-surfaces into weighted projective spaces
Let V be a normal affine surface which admits a C*- and a C+-action. In this note we show that in many cases V can be embedded as a principal Zariski open subset into a hypersurface of a weighted projective space. In particular, we recover a result of D. Daigle and P. Russell
Smooth affine surfaces with non-unique C*-actions
In this paper we complete the classification of effective C*-actions on smooth affine surfaces up to conjugation in the full automorphism group and up to inversion of C*. If a smooth affine surface V admits more than one C*-action then it is known to be Gizatullin i.e., it can be completed by a linear chain of smooth rational curves. In our previous paper we gave a sufficient condition, in terms of the Dolgachev- Pinkham-Demazure (or DPD) presentation, for the uniqueness of a C*-action on a Gizatullin surface. In the present paper we show that this condition is also necessary, at least in the smooth case. In fact, if the uniqueness fails for a smooth Gizatullin surface V which is neither toric nor Danilov-Gizatullin, then V admits a continuous family of pairwise non-conjugated C*-actions depending on one or two parameters. We give an explicit description of all such surfaces and their C*-actions in terms of DPD presentations. We also show that for every k > 0 one can find a Danilov- Gizatullin surface V (n) of index n = n(k) with a family of pairwise non-conjugate C+-actions depending on k parameters
Flexible varieties and automorphism groups
Given an affine algebraic variety X of dimension at least 2, we let SAut (X)
denote the special automorphism group of X i.e., the subgroup of the full
automorphism group Aut (X) generated by all one-parameter unipotent subgroups.
We show that if SAut (X) is transitive on the smooth locus of X then it is
infinitely transitive on this locus. In turn, the transitivity is equivalent to
the flexibility of X. The latter means that for every smooth point x of X the
tangent space at x is spanned by the velocity vectors of one-parameter
unipotent subgroups of Aut (X). We provide also different variations and
applications.Comment: Final version; to appear in Duke Math.
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
Relaxation in a glassy binary mixture: Mode-coupling-like power laws, dynamic heterogeneity and a new non-Gaussian parameter
We examine the relaxation of the Kob-Andersen Lennard-Jones binary mixture
using Brownian dynamics computer simulations. We find that in accordance with
mode-coupling theory the self-diffusion coefficient and the relaxation time
show power-law dependence on temperature. However, different mode-coupling
temperatures and power laws can be obtained from the simulation data depending
on the range of temperatures chosen for the power-law fits. The temperature
that is commonly reported as this system's mode-coupling transition
temperature, in addition to being obtained from a power law fit, is a crossover
temperature at which there is a change in the dynamics from the high
temperature homogeneous, diffusive relaxation to a heterogeneous, hopping-like
motion. The hopping-like motion is evident in the probability distributions of
the logarithm of single-particle displacements: approaching the commonly
reported mode-coupling temperature these distributions start exhibiting two
peaks. Notably, the temperature at which the hopping-like motion appears for
the smaller particles is slightly higher than that at which the hopping-like
motion appears for the larger ones. We define and calculate a new non-Gaussian
parameter whose maximum occurs approximately at the time at which the two peaks
in the probability distribution of the logarithm of displacements are most
evident.Comment: Submitted for publication in Phys. Rev.
Boosting Image Forgery Detection using Resampling Features and Copy-move analysis
Realistic image forgeries involve a combination of splicing, resampling,
cloning, region removal and other methods. While resampling detection
algorithms are effective in detecting splicing and resampling, copy-move
detection algorithms excel in detecting cloning and region removal. In this
paper, we combine these complementary approaches in a way that boosts the
overall accuracy of image manipulation detection. We use the copy-move
detection method as a pre-filtering step and pass those images that are
classified as untampered to a deep learning based resampling detection
framework. Experimental results on various datasets including the 2017 NIST
Nimble Challenge Evaluation dataset comprising nearly 10,000 pristine and
tampered images shows that there is a consistent increase of 8%-10% in
detection rates, when copy-move algorithm is combined with different resampling
detection algorithms
Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers
We use a long, all-atom molecular dynamics (MD) simulation combined with
theoretical modeling to investigate the dynamics of selected lipid atoms and
lipid molecules in a hydrated diyristoyl-phosphatidylcholine (DMPC) lipid
bilayer. From the analysis of a 0.1 s MD trajectory we find that the time
evolution of the mean square displacement, [\delta{r}(t)]^2, of lipid atoms and
molecules exhibits three well separated dynamical regions: (i) ballistic, with
[\delta{r}(t)]^2 ~ t^2 for t < 10 fs; (ii) subdiffusive, with [\delta{r}(t)]^2
~ t^{\beta} with \beta<1, for 10 ps < t < 10 ns; and (iii) Fickian diffusion,
with [\delta{r}(t)]^2 ~ t for t > 30 ns. We propose a memory function approach
for calculating [\delta{r}(t)]^2 over the entire time range extending from the
ballistic to the Fickian diffusion regimes. The results are in very good
agreement with the ones from the MD simulations. We also examine the
implications of the presence of the subdiffusive dynamics of lipids on the
self-intermediate scattering function and the incoherent dynamics structure
factor measured in neutron scattering experiments.Comment: Submitted to Phys. Rev.
Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems
Computer modeling of multicellular systems has been a valuable tool for
interpreting and guiding in vitro experiments relevant to embryonic
morphogenesis, tumor growth, angiogenesis and, lately, structure formation
following the printing of cell aggregates as bioink particles. Computer
simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in
explaining and predicting the resulting stationary structures (corresponding to
the lowest adhesion energy state). Here we present two alternatives to the MMC
approach for modeling cellular motion and self-assembly: (1) a kinetic Monte
Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC,
both KMC and CPD methods are capable of simulating the dynamics of the cellular
system in real time. In the KMC approach a transition rate is associated with
possible rearrangements of the cellular system, and the corresponding time
evolution is expressed in terms of these rates. In the CPD approach cells are
modeled as interacting cellular particles (CPs) and the time evolution of the
multicellular system is determined by integrating the equations of motion of
all CPs. The KMC and CPD methods are tested and compared by simulating two
experimentally well known phenomena: (1) cell-sorting within an aggregate
formed by two types of cells with different adhesivities, and (2) fusion of two
spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev
Resampling Forgery Detection Using Deep Learning and A-Contrario Analysis
The amount of digital imagery recorded has recently grown exponentially, and
with the advancement of software, such as Photoshop or Gimp, it has become
easier to manipulate images. However, most images on the internet have not been
manipulated and any automated manipulation detection algorithm must carefully
control the false alarm rate. In this paper we discuss a method to
automatically detect local resampling using deep learning while controlling the
false alarm rate using a-contrario analysis. The automated procedure consists
of three primary steps. First, resampling features are calculated for image
blocks. A deep learning classifier is then used to generate a heatmap that
indicates if the image block has been resampled. We expect some of these blocks
to be falsely identified as resampled. We use a-contrario hypothesis testing to
both identify if the patterns of the manipulated blocks indicate if the image
has been tampered with and to localize the manipulation. We demonstrate that
this strategy is effective in indicating if an image has been manipulated and
localizing the manipulations.Comment: arXiv admin note: text overlap with arXiv:1802.0315
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